Modeling, simulation and optimal control strategy for batch fermentation processes

The use of fermenters at large scale is usually hampered by sub-optimal conditions in terms of yield and productivity, along with the low tolerance of strains to process stresses, such as substrate and product toxicity, and other fermentation inhibitors. Attempts to improve the industrial efcacy of fermenters have been in the areas of genetic engineering to improve strain tolerance, but this usually involves detailed and unfeasible mechanistic studies. Statistical designs of experiments have also been used to optimize industrial fermenters but this again often results in local optima due to the relatively small-dimensional space covered by the experiments. Mathematical techniques have recorded great successes and regarding ethanol fermentation with sorghum extracts, previous work has modeled and established the presence of product inhibition, however, did not consider other degrees of freedom (temperature and pH) that minimize the efect of such inhibitions. This paper includes the description of a batch alcohol fermentation process that has been optimized using a technique based on the application of mathematical modeling and optimal control. Calculus of variation is introduced as a valuable tool to derive and solve the necessary conditions for optimality, and the obtained results show the optimal temperature and pH profles for the fermentation of sorghum extracts. A Simulink model of the fermentation process shows that using the proposed control strategy increases ethanol yield by 14.18%, cell growth by 71.96% decreases the residual substrate by 84.77%.